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Essentials of Statistics for the Behavioral Sciences - Coggle Diagram
Essentials of Statistics for the Behavioral Sciences
Chapter 10: Introduction to the t Statistic
Purpose of the t Statistic
Used when population standard deviation is unknown
Uses sample information to estimate population values
Allows hypothesis testing with limited information
t Distribution
Similar to normal distribution
Has greater variability in the tails
Changes shape based on sample size
Approaches normal distribution as sample size increases
Degrees of Freedom
Determined by sample size
Equal to n − 1 for one-sample t tests
Affects shape of t distribution
Estimating Population Variability
Uses sample variance
Uses sample standard deviation
Creates estimated standard error
Hypothesis Testing with t
Compare sample mean to population mean
Evaluate whether difference is due to chance
Use critical values from t distribution
Decision Making
Reject null hypothesis when t is in critical region
Fail to reject null hypothesis when evidence is insufficient
Relationship to Chapter 9
Extends hypothesis testing when σ is unknown
Uses sample estimates instead of population parameters
Chapter 12: Independent-Measures t Test
Purpose
Compare means from two separate groups
Determine whether group differences are significant
Null Hypothesis
No difference between population means
Alternative Hypothesis
Population means are different
Mean Difference
Calculated between group averages
Evaluated relative to variability
Pooled Variance
Combines variability from both samples
Provides estimate of population variance
Standard Error Difference
Measures expected variation between sample means
Degrees of Freedom
Based on both sample sizes
Applications
Comparing teaching methods
Comparing treatment groups
Comparing counseling approaches
Interpretation
Large t values indicate stronger evidence against H₀
Chapter 14: Analysis of Variance (ANOVA)
Purpose
Compare three or more group means
Avoid multiple t tests
Analysis of Variance
Separates variability into components
Examines sources of differences
Between-Treatments Variance
Differences caused by treatment conditions
Reflects effects of independent variable
Within-Treatments Variance
Random differences among individuals
Represents chance variation
F Ratio
Compares between-group variance to within-group variance
Larger F suggests treatment effect
Null Hypothesis
All population means are equal
Alternative Hypothesis
At least one mean differs
Advantages of ANOVA
Reduces Type I error
Efficient for multiple groups
Applications
Comparing multiple therapies
Comparing teaching strategies
Comparing age groups
Post Hoc Tests
Used after significant ANOVA
Identify which groups differ
Relationship to t Tests
ANOVA extends comparison to three or more group